Cholera

Here we keep the results of various numerical experiments of optimal control outcomes in the Cholera model. Specifically, we focus on the difference between the optimal strategy, when control is customized to each patch versus the “one size fits all strategy” where both patches are forced to be given the same control.

Experiment 0 (no movement between patches)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 mu2 beta_I1 beta_I2 beta_W1 beta_W2 v1 v2 u1 u2 m1 m2 n1 n2 gamma1 gamma2
0 0 2.64e-06 2.64e-06 1.01e-05 1.01e-05 0 0 0 0 0 0 0 0 0.25 0.25
delta1 delta2 xi1 xi2 nu1 nu2 rho1 rho2
5e-04 5e-04 0.00756 0.00756 0.00756 0.00756 0.025 0.025

Initial conditions:

S1 S2 I1 I2 R1 R2 W1 W2
92791 94406 1609 1440 5589 4145 118 120

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 D1 D2 eta1 eta2 tol control_type
1 1 0.125 0.125 10000 10000 0.0125 0.0125 1000 1000 0.01 unique
v1_min v1_max v2_min v2_max u1_min u1_max u2_min u2_max
0 0.015 0 0.015 0 0.4 0 0.4

With these parameters, the system has an R0 of about 1.9898893.

No control

Time 0 corresponds to 100 days since the start of the outbreak.

Vaccination Only

We consider the case with only vaccination (no sanitation).

Controls start at day 100.

Sanitation Only

We also consider the case with only sanitation (no vaccination).

Controls start at day 100`.

Both Vaccination and Sanitation

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 1 (symmetric, m1=m2=0.05)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 mu2 beta_I1 beta_I2 beta_W1 beta_W2 v1 v2 u1 u2 m1 m2 n1 n2 gamma1 gamma2
0 0 2.6e-06 2.6e-06 1.01e-05 1.01e-05 0 0 0 0 0.05 0.05 0 0 0.25 0.25
delta1 delta2 xi1 xi2 nu1 nu2 rho1 rho2
5e-04 5e-04 0.00756 0.00756 0.00756 0.00756 0.025 0.025

Initial conditions: need to re-calculate initial conditions with movement

S1 S2 I1 I2 R1 R2 W1 W2
92791 94406 1609 1440 5589 4145 118 120

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 D1 D2 eta1 eta2 tol control_type
1 1 0.125 0.125 10000 10000 0.0125 0.0125 1000 1000 0.01 unique
v1_min v1_max v2_min v2_max u1_min u1_max u2_min u2_max
0 0.015 0 0.015 0 0.4 0 0.4

With these parameters, the system has an R0 of about 1.9898893.

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no sanitation).

Controls start at day 100.

Sanitation Only

We also consider the case with only sanitation (no vaccination).

Controls start at day 100`.

Both Vaccination and Sanitation

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 2 (symmetric movement, m1=m2=0.1)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 mu2 beta_I1 beta_I2 beta_W1 beta_W2 v1 v2 u1 u2 m1 m2 n1 n2 gamma1 gamma2
0 0 2.6e-06 2.6e-06 1.01e-05 1.01e-05 0 0 0 0 0.1 0.1 0 0 0.25 0.25
delta1 delta2 xi1 xi2 nu1 nu2 rho1 rho2
5e-04 5e-04 0.00756 0.00756 0.00756 0.00756 0.025 0.025

Initial conditions: need to re-calculate initial conditions with movement

S1 S2 I1 I2 R1 R2 W1 W2
92791 94406 1609 1440 5589 4145 118 120

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 D1 D2 eta1 eta2 tol control_type
1 1 0.125 0.125 10000 10000 0.0125 0.0125 1000 1000 0.01 unique
v1_min v1_max v2_min v2_max u1_min u1_max u2_min u2_max
0 0.015 0 0.015 0 0.4 0 0.4

With these parameters, the system has an R0 of about 1.9898893.

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no sanitation).

Controls start at day 100.

Sanitation Only

We also consider the case with only sanitation (no vaccination).

Controls start at day 100`.

Both Vaccination and Sanitation

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 3 (asymmetric movement, m1=0.05, m2=0.1)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 mu2 beta_I1 beta_I2 beta_W1 beta_W2 v1 v2 u1 u2 m1 m2 n1 n2 gamma1 gamma2
0 0 2.6e-06 2.6e-06 1.01e-05 1.01e-05 0 0 0 0 0.05 0.1 0 0 0.25 0.25
delta1 delta2 xi1 xi2 nu1 nu2 rho1 rho2
5e-04 5e-04 0.00756 0.00756 0.00756 0.00756 0.025 0.025

Initial conditions: need to re-calculate initial conditions with movement

S1 S2 I1 I2 R1 R2 W1 W2
92791 94406 1609 1440 5589 4145 118 120

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 D1 D2 eta1 eta2 tol control_type
1 1 0.125 0.125 10000 10000 0.0125 0.0125 1000 1000 0.01 unique
v1_min v1_max v2_min v2_max u1_min u1_max u2_min u2_max
0 0.015 0 0.015 0 0.4 0 0.4

With these parameters, the system has an R0 of about 1.9898893.

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no sanitation).

Controls start at day 100.

Sanitation Only

We also consider the case with only sanitation (no vaccination).

Controls start at day 100`.

Both Vaccination and Sanitation

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 4 (asymmetric movement, m1=0.1, m2 =0.05)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 mu2 beta_I1 beta_I2 beta_W1 beta_W2 v1 v2 u1 u2 m1 m2 n1 n2 gamma1 gamma2
0 0 2.6e-06 2.6e-06 1.01e-05 1.01e-05 0 0 0 0 0.05 0.1 0 0 0.25 0.25
delta1 delta2 xi1 xi2 nu1 nu2 rho1 rho2
5e-04 5e-04 0.00756 0.00756 0.00756 0.00756 0.025 0.025

Initial conditions: need to re-calculate initial conditions with movement

S1 S2 I1 I2 R1 R2 W1 W2
92791 94406 1609 1440 5589 4145 118 120

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 D1 D2 eta1 eta2 tol control_type
1 1 0.125 0.125 10000 10000 0.0125 0.0125 1000 1000 0.01 unique
v1_min v1_max v2_min v2_max u1_min u1_max u2_min u2_max
0 0.015 0 0.015 0 0.4 0 0.4

With these parameters, the system has an R0 of about 1.9898893.

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no sanitation).

Controls start at day 100.

Sanitation Only

We also consider the case with only sanitation (no vaccination).

Controls start at day 100`.

Both Vaccination and Sanitation

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Ebola

We show similar results instead employing the Ebola model.

Experiment 0 (no movement between patches)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 alpha1 gammaI1 gammaH1 phi1 deltaI1 deltaH1 xi1 m1 n1
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 1e-05 0
mu2 alpha2 gammaI2 gammaH2 phi2 deltaI2 deltaH2 xi2 m2 n2
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 0.001 0

Initial conditions:

S1 E1 I1 H1 D1 R1 S2 E2 I2 H2 D2 R2
99300 400 300 0 0 0 1e+05 0 0 0 0 0

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 control_type tol v1 v2
1 1 0.01 0.01 50000 50000 uniform 0.01 0 0
v1_min v1_max v2_min v2_max betaI1 betaI2 betaD1 betaD2 N1 N2
0 0.015 0 0.015 1e-07 1e-07 5.94e-05 5.94e-05 1e+05 1e+05

Need to add Ebola R0 calculation

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no TBD).

Controls start at day 100.

TBD Only

We also consider the case with only TBD (no vaccination).

Controls start at day 100`.

Both Vaccination and TBD

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 1 (symmetric, m1=m2=0.05)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 alpha1 gammaI1 gammaH1 phi1 deltaI1 deltaH1 xi1 m1 n1
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 1e-05 0
mu2 alpha2 gammaI2 gammaH2 phi2 deltaI2 deltaH2 xi2 m2 n2
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 0.001 0

Initial conditions:

S1 E1 I1 H1 D1 R1 S2 E2 I2 H2 D2 R2
99300 400 300 0 0 0 1e+05 0 0 0 0 0

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 control_type tol v1 v2
1 1 0.01 0.01 50000 50000 uniform 0.01 0 0
v1_min v1_max v2_min v2_max betaI1 betaI2 betaD1 betaD2 N1 N2
0 0.015 0 0.015 1e-07 1e-07 5.94e-05 5.94e-05 1e+05 1e+05

Need to add Ebola R0 calculation

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no TBD).

Controls start at day 100.

TBD Only

We also consider the case with only TBD (no vaccination).

Controls start at day 100`.

Both Vaccination and TBD

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 2 (symmetric, m1=m2=0.1)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 alpha1 gammaI1 gammaH1 phi1 deltaI1 deltaH1 xi1 m1 n1
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 1e-05 0
mu2 alpha2 gammaI2 gammaH2 phi2 deltaI2 deltaH2 xi2 m2 n2
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 0.001 0

Initial conditions:

S1 E1 I1 H1 D1 R1 S2 E2 I2 H2 D2 R2
99300 400 300 0 0 0 1e+05 0 0 0 0 0

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 control_type tol v1 v2
1 1 0.01 0.01 50000 50000 uniform 0.01 0 0
v1_min v1_max v2_min v2_max betaI1 betaI2 betaD1 betaD2 N1 N2
0 0.015 0 0.015 1e-07 1e-07 5.94e-05 5.94e-05 1e+05 1e+05

Need to add Ebola R0 calculation

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no TBD).

Controls start at day 100.

TBD Only

We also consider the case with only TBD (no vaccination).

Controls start at day 100`.

Both Vaccination and TBD

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 3 (asymmetric, m1=.05, m2=0.1)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 alpha1 gammaI1 gammaH1 phi1 deltaI1 deltaH1 xi1 m1 n1
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 1e-05 0
mu2 alpha2 gammaI2 gammaH2 phi2 deltaI2 deltaH2 xi2 m2 n2
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 0.001 0

Initial conditions:

S1 E1 I1 H1 D1 R1 S2 E2 I2 H2 D2 R2
99300 400 300 0 0 0 1e+05 0 0 0 0 0

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 control_type tol v1 v2
1 1 0.01 0.01 50000 50000 uniform 0.01 0 0
v1_min v1_max v2_min v2_max betaI1 betaI2 betaD1 betaD2 N1 N2
0 0.015 0 0.015 1e-07 1e-07 5.94e-05 5.94e-05 1e+05 1e+05

Need to add Ebola R0 calculation

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no TBD).

Controls start at day 100.

TBD Only

We also consider the case with only TBD (no vaccination).

Controls start at day 100`.

Both Vaccination and TBD

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.

Experiment 4 (asymmetric, m1=.1, m2=0.05)

Parameters

The following experiments use these parameters and initial conditions.

Parameters:

mu1 alpha1 gammaI1 gammaH1 phi1 deltaI1 deltaH1 xi1 m1 n1
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 1e-05 0
mu2 alpha2 gammaI2 gammaH2 phi2 deltaI2 deltaH2 xi2 m2 n2
5.5e-05 0.1 0.0666667 0.028 0.236 0.024 0.01 0.222 0.001 0

Initial conditions:

S1 E1 I1 H1 D1 R1 S2 E2 I2 H2 D2 R2
99300 400 300 0 0 0 1e+05 0 0 0 0 0

Optimal control parameters:

b1 b2 C1 C2 epsilon1 epsilon2 control_type tol v1 v2
1 1 0.01 0.01 50000 50000 uniform 0.01 0 0
v1_min v1_max v2_min v2_max betaI1 betaI2 betaD1 betaD2 N1 N2
0 0.015 0 0.015 1e-07 1e-07 5.94e-05 5.94e-05 1e+05 1e+05

Need to add Ebola R0 calculation

No control

Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement

Vaccination Only

We consider the case with only vaccination (no TBD).

Controls start at day 100.

TBD Only

We also consider the case with only TBD (no vaccination).

Controls start at day 100`.

Both Vaccination and TBD

Lastly, we show how results change if we optimize both controls.

Controls start at day 100.